1 votes 1 votes How many non zero entries does the matrix representing relation $R$ on a set $A$ = $\left \{ 1,2,3,4,5,6....1000 \right \}$. a. $R = \left \{ (x,y) \; | x = y \pm 1 \right \}$ b. $R = \left \{ (x,y) \; | x + y = 1000 \right \}$ Set Theory & Algebra relations discrete-mathematics + – dd asked Dec 14, 2016 dd 1.8k views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
Best answer 1 votes 1 votes A. R = { (1,2),(2,3),(3,4),...,(n-1,n) } Union Reverse of former. Total combinations = 2*(n-1) = 1998. B. R = = { (1,n-1),(2,n-2),(3,n-3),...,(n-1,1) Total combinations = n-1 = 999. Aghori answered Dec 14, 2016 selected Dec 23, 2016 by Sushant Gokhale Aghori comment Share Follow See all 0 reply Please log in or register to add a comment.